Lesson 24a - Absolute Conditional Convergence

1 n b n thismeansthattheabsoluteseriesconvergesby

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Unformatted text preview: test as: n 3 2n 1 n 2 an lim lim 5 n b n n 3n 2 2 1 n n 5 2n 3 n 2 an lim lim 5 n b n n 3n 2 2 n n 5 2n 3 n 2 5 5 5 an lim lim n 5 n 2 n n b n n 3n 2 n 5 5 5 n n n 2 1 1 2 3 a n lim n lim n n b n 3 2 n 1 3 5 n n a lim n 1 n b n This means that the absolute series converges by limit comparison test (1<infinity). This means the series is absolutely convergent. Example 2 Determine if the following series converges absolutely, conditionally, or diverges: n (1) n n2 e n Here we can see that the limit as n infinity produces: en en lim ( ) lim ( ) n n...
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This note was uploaded on 02/07/2014 for the course MATH 1004 taught by Professor Mark during the Summer '00 term at Carleton CA.

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